Question

In YDSE, coherent monochromatic light having wavelength $600nm$ falls on the slits. First-order bright fringe is at $4.84$mm from central maxima. Determine the wavelength for which the first-order dark fringe will be observed at the same location on screen. (Take $D=3m$)

• A. $600nm$
• B. $1200nm$
• C. $300nm$
• D. $900nm$

Answer 1

The correct option is B $1200nm$

$\beta =\lambda \frac{D}{d}$

=> $4.84\ast {10}^{-3}=600\ast {10}^{-9}\frac{D}{d}$

=>$\frac{D}{d}=\frac{4.84}{6}{10}^4$

Case 2,

If first order dark fringe is observed at $4.84mm$ then $\beta =2\ast 4.84=9.68mm$

$\lambda =\beta \frac{d}{D}$

=>$\lambda =4.84\ast {10}^{-3}\frac{d}{D}=1200nm$

Answer. B) 1200 nm